Pith Number

pith:VA3632NE

pith:2026:VA3632NEYL2RGOHO3VUA4OB4HK

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Block-equivalent finite Gabor frames

Laura De Carli, Luis Rodriguez, Oleg Asipchuk

Finite Gabor systems are block-equivalent when either the modulation set or the translation set is a subgroup of Z_N.

arxiv:2605.16139 v1 · 2026-05-15 · math.FA

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Claims

C1strongest claim

We show that a Gabor system G=G(g,L×K)⊂C^N is block-equivalent when either the modulation set L or the translation set K is a subgroup of Z_N. We also characterize situations in which the frame operator matrix becomes diagonal.

C2weakest assumption

The unitary transformations achieving the block-diagonal form are both explicit and computationally efficient, as required by the definition of block-equivalence; this premise enters when the authors invoke the subgroup property to construct the equivalence.

C3one line summary

Gabor systems in C^N with subgroup modulation or translation sets have frame operators that are unitarily equivalent to block-diagonal matrices, with further diagonal and sparsity results under geometric conditions.

References

23 extracted · 23 resolved · 0 Pith anchors

[1] L. D. Abreu, P. Balazs, N. Holighaus, F. Luef, and M. Speckbacher,Time-frequency analysis on flat tori and Gabor frames in finite dimensions, Applied and Computa- tional Harmonic Analysis, vol. 69, 20 2024

[2] E. J. Barbeau,Polynomials, Springer, New York, 1989 1989

[3] J. J. Benedetto and M. Fickus,Finite normalized tight frames, Advances in Compu- tational Mathematics, vol. 18, no. 2–4, 2003, pp. 357–385 2003

[4] Christensen,An Introduction to Frames and Riesz Bases, 2nd edition, Birkh¨ auser, Boston, 2016 2016

[5] E. M. Coven and A. Meyerowitz,Tiling the integers with translates of one finite set, Journal of Algebra, vol. 212, no. 1, 1999, pp. 161–174 1999

Receipt and verification

First computed	2026-05-20T00:01:54.672327Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a837ede9a4c2f51338eedd680e383c3aad9af8a4311b8c6ce6becf7b07b12fde

Aliases

arxiv: 2605.16139 · arxiv_version: 2605.16139v1 · doi: 10.48550/arxiv.2605.16139 · pith_short_12: VA3632NEYL2R · pith_short_16: VA3632NEYL2RGOHO · pith_short_8: VA3632NE

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/VA3632NEYL2RGOHO3VUA4OB4HK \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: a837ede9a4c2f51338eedd680e383c3aad9af8a4311b8c6ce6becf7b07b12fde

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "18895bfaa1910b53fa8cb604c29a7b979193458d9c5a6f5d9a53993a17c90271",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2026-05-15T16:19:19Z",
    "title_canon_sha256": "53e0adeb2d30e06d249a971b53903c59c50f170d5e357eb7834a2efcc4f473ab"
  },
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  "source": {
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    "kind": "arxiv",
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}